Novičenko Viktor, Ratas Irmantas
Faculty of Physics, Vilnius University, Saulėtekio ave. 3, LT-10222 Vilnius, Lithuania.
Center for Physical Sciences and Technology, Saulėtekio ave. 3, LT-10222 Vilnius, Lithuania.
Chaos. 2021 Sep;31(9):093138. doi: 10.1063/5.0033391.
Weakly coupled limit cycle oscillators can be reduced into a system of weakly coupled phase models. These phase models are helpful to analyze the synchronization phenomena. For example, a phase model of two oscillators has a one-dimensional differential equation for the evolution of the phase difference. The existence of fixed points determines frequency-locking solutions. By treating each oscillator as a black-box possessing a single input and a single output, one can investigate various control algorithms to change the synchronization of the oscillators. In particular, we are interested in a delayed feedback control algorithm. Application of this algorithm to the oscillators after a subsequent phase reduction should give the same phase model as in the control-free case, but with a rescaled coupling strength. The conventional delayed feedback control is limited to the change of magnitude but does not allow the change of sign of the coupling strength. In this work, we present a modification of the delayed feedback algorithm supplemented by an additional unstable degree of freedom, which is able to change the sign of the coupling strength. Various numerical calculations performed with Landau-Stuart and FitzHugh-Nagumo oscillators show successful switching between an in-phase and anti-phase synchronization using the provided control algorithm. Additionally, we show that the control force becomes non-invasive if our objective is stabilization of an unstable phase difference for two coupled oscillators.
弱耦合极限环振荡器可以简化为弱耦合相位模型系统。这些相位模型有助于分析同步现象。例如，两个振荡器的相位模型有一个用于相位差演化的一维微分方程。不动点的存在决定了锁频解。通过将每个振荡器视为具有单个输入和单个输出的黑箱，可以研究各种控制算法来改变振荡器的同步。特别地，我们对一种延迟反馈控制算法感兴趣。在后续相位简化后将该算法应用于振荡器应该会得到与无控制情况相同的相位模型，但耦合强度会重新缩放。传统的延迟反馈控制仅限于幅度的变化，不允许耦合强度的符号改变。在这项工作中，我们提出了一种对延迟反馈算法的修改，补充了一个额外的不稳定自由度，它能够改变耦合强度的符号。使用朗道 - 斯图尔特振荡器和菲茨休 - 纳古莫振荡器进行的各种数值计算表明，使用所提供的控制算法能够在同相和反相同步之间成功切换。此外，我们表明，如果我们的目标是稳定两个耦合振荡器的不稳定相位差，那么控制力将变得无创。
